Related papers: Multivariate COGARCH(1,1) processes
The covariance matrix is formulated in the framework of a linear multivariate ARCH process with long memory, where the natural cross product structure of the covariance is generalized by adding two linear terms with their respective…
We describe spatio-temporal random processes using linear mixed models. We show how many commonly used models can be viewed as special cases of this general framework and pay close attention to models with separable or product-sum…
Bayesian analysis of state-space models includes computing the posterior distribution of the system's parameters as well as filtering, smoothing, and predicting the system's latent states. When the latent states wander around $\mathbb{R}^n$…
In this paper, we examine continuous-time autoregressive moving-average (CARMA) processes on Banach spaces driven by L\'evy subordinators. We show their existence and cone-invariance, investigate their first and second order moment…
We present an outline of the theory of certain L\'evy-driven, multivariate stochastic processes, where the processes are represented by rational transfer functions (Continuous-time AutoRegressive Moving Average or CARMA models) and their…
We analyze multivariate ordered discrete response models with a lattice structure, modeling decision makers who narrowly bracket choices across multiple dimensions. These models map latent continuous processes into discrete responses using…
We present a general class of spatio-temporal stochastic processes describing the causal evolution of a positive-valued field in space and time. The field construction is based on independently scattered random measures of Levy type whose…
In this manuscript, we analytically and numerically study statistical properties of an heteroskedastic process based on the celebrated ARCH generator of random variables whose variance is defined by a memory of $q_{m}$-exponencial, form…
We show that stochastic processes with linear conditional expectations and quadratic conditional variances are Markov, and their transition probabilities are related to a three-parameter family of orthogonal polynomials which generalize the…
The AutoRegressive Conditional Heteroskedasticity (ARCH) and its generalized version (GARCH) family of models have grown to encompass a wide range of specifications, each of them is designed to enhance the ability of the model to capture…
We study continuous-time Markov chains on the non-negative integers under mild regularity conditions (in particular, the set of jump vectors is finite and both forward and backward jumps are possible). Based on the so-called flux balance…
This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence $(c_0,c_1,\dots,c_n)$ of covariance lags $c_k=\mathbb{E}\{y(t+k)\overline{y(t)}\}$ emanating from a stationary periodic…
A novel first-order moving-average model for analyzing time series observed at irregularly spaced intervals is introduced. Two definitions are presented, which are equivalent under Gaussianity. The first one relies on normally distributed…
Estimation of covariance matrices is a fundamental problem in multivariate statistics. Recently, growing efforts have focused on incorporating covariate effects into these matrices, facilitating subject-specific estimation. Despite these…
Numerous studies grounded on Hawkes processes have been carried out in many fields including finance, biology and social network. Hawkes processes form a class of selfexciting simple point processes. In this article, we consider a general…
We consider estimation of covariance matrices and their inverses (a.k.a. precision matrices) for high-dimensional stationary and locally stationary time series. In the latter case the covariance matrices evolve smoothly in time, thus…
The covariance of a stationary process $X$ is diagonalized by a Fourier transform. It does not take into account the complex Fourier phase and defines Gaussian maximum entropy models. We introduce a general family of phase harmonic…
We study a class of stationary processes indexed by $\Z^d$ that are defined via minors of $d$-dimensional (multilevel) Toeplitz matrices. We obtain necessary and sufficient conditions for phase multiplicity (the existence of a phase…
In this paper we show that stationary and non-stationary multivariate continuous-time ARMA (MCARMA) processes have the representation as a sum of multivariate complex-valued Ornstein-Uhlenbeck processes under some mild assumptions. The…
The higher dimensional autoregressive models would describe some of the econometric processes relatively generically if they incorporate the heterogeneity in dependence on times. This paper analyzes the stationarity of an autoregressive…